一类含有预防接种的SVIR最优控制模型

Optimal Control and Stability Analysis of an Epidemic Model with Vaccination

建立一个含有预防接种的SVIR最优控制模型.首先求出基本再生数.当R0<1时,无病平衡点是局部渐近稳定以及全局渐近稳定的;当R0>1时,地方病平衡点是局部渐近稳定的.其次建立目标函数,利用Pontryagin最大值原理得到最优变量控制组.最后数值模拟的结果验证了最优控制率的有效性.

In this paper ,an optimal control model of SVIR based on vaccination is constructed and ana‐lyzed .First ,we show that if the basic reproduction number R0 < 1 ,the disease‐free equilibrium is locally asymptotically stable and globally asymptotically stable ,and that if R0 > 1 ,the disease‐free equilibrium becomes un‐stable ,while the endemic equilibrium is locally asymptotically stable .Next ,we establish the objective function and the optimal control pair with the help of the Pon‐trjagin maximum principle .Final‐ly ,we make a numerical simulation to verify the validity of the optimal control strategy ,and the results indicate that vaccination is of great practical importance after an infectious disease outbreak .